The sum of $6$ consecutive even numbers is $126$. What is the fourth number in this sequence?
Solution: Call the first number in the sequence $x$. The next even number in the sequence is $x + 2$ The sum of the $6$ consecutive even numbers is: $x+ (x + 2)+ (x + 4)+ (x + 6)+ (x + 8)+ (x + 10) = 126$ $6x + 30= 126$ $6x = 96$ $x = 16$ Since $x$ is the first number, $x + 6$ is the fourth even number. Thus, the fourth number in the sequence is $22$.